Wednesday, 14 December 2016

Armada Dice part II: Squadron to Ship

With wave 5 on the horizon, I want to put into context the stats for the squadron we already have. As everyone has seen, wave 3 has made a very powerful impact on the squadron game in Armada, because of the cheap activations, cheap squadron pushers and Bomber Command Center.

With the aid of a script I made, I can accurately calculate the damage based on clever ability usage. What does clever ability usage mean? It means not choosing the best order in which to resolve abilities, based on the initial roll

The aim of this blog post is two-fold: to show that there are clever paths to be taken when rerolling with simple rules of thumb that can be followed; to rank bombers based on their effectiveness taking into account the effect of Bomber Command Center and their cost.

X-wings

X-wings are the lowest efficiency bombers currently in the game, with only one red dice. Bomber Command Center in their case helps bring them in line with Y-wing in terms of expected damage. An X-wing with 2 Bomber Command Centers will do an average of 1.15 average damage, as opposed to a naked Y-wing which does 1. Of course, the efficiency is nowhere near, since the X-wing is 30% more expensive.

What about rerolls? With an X-wing and one BCC, you're only expected to reroll Accuracies and Blanks to get the best average result. In the diagram below, the center is the starting point, with the 5 possibilities of the red dice roll. On the next level, the red line represents the best choice, which is rerolling only in the case of the blank or accuracy.

What if we have 2 BCCs? Then the correct answer becomes rerolling all non-doubles on the first reroll, followed by blanks on the second roll. All in all, easy to remember!

To remember: While the X-wings have the lowest damage overall of all bombers, they benefit from having Bomber Command Center the most! 2BCCs increase their anti-ship damage by 50%!

Y-wings/TIE Bombers

Y-wings are the Rebel's cheap, no-fuss bomber option. 1 average damage with 1BCC, up to 1.25 and 1.44 with 2 BCCs! 44% damage increase is still very good! The TIE Bomber has of course the same damage output, but with fewer fleet points, so with greater overall efficiency in terms of anti-ship combat.

What about rerolls? Turns out this is more complicated. The average being 1, if you have a single reroll and you rolled a Hit, you have 2 options:

You are at average, be content with the result

Try your luck and go for the Hit/Crit

Both have the same average result, but the second option plays with variance a bit more, while the first option is safe!

If you have 2 rerolls, you can safely reroll Hits on the first reroll, followed by only-blank rerolls on the second reroll for safest and best average result!

Rule of thumb: No matter how many black dice rerolls you have, you can safely reroll hits on any reroll but the last! The last reroll is the one where you make the choice between safe and trying your luck! (but still with the same average result)

Firesprays

Almost not worth mentioning, since the rerolls are extremely intuitive. Anything that isn't a damage you can reroll. Overall they gain 30% damage from having 2BCCs.

B-wings

With B-wings things get interesting. In terms of damage, they have the highest totals of any unnamed squadron and overall incredible efficiency.

As to rerolls, the priority seems to be the black dice. First make sure you have at least a Hit on that, then reroll the accuracy if you have rolled one. In the image below, all non-optimal choices and their respective consequences have been eliminated, so a red edge represents a correct choice. If there are two red edges, that means that both choices carry exactly the same weight, meaning they come out with the same average damage, no matter what.

Keyan is a special example (and now Ten Numb), because they're the only ones with 2 black dice and Keyan has a reroll capability built in! Keyan benefits little, only 13% for a single BCC and 22.40% for 2 BCCs, but it takes him to an incredible 3 average damage!

His reroll rule of thumb is similar to Y-wings: Reroll Hits as long as you have rerolls left, otherwise reroll only blanks if you want to keep it safe!

Efficiency

So where does this take us? I have arranged the following table, where red columns are average damage, blue columns are benefits comparing to the vanilla scenario and white columns are efficiency, which I have defined as average damage per 10 points of squadron of that type. In this first table you can see how the X-wing gets to 1.15 average damage, trumping the vanilla Y-wing and TIE Bomber at 1 damage.

Default

1BCC

2BCC

Avg

Avg/10p

Avg

Benefit

Avg/10p

Avg

Benefit

Avg/10p

1red (X-wing)

0.75

0.58

1.03

37.33%

0.79

1.15

53.33%

0.88

1black (Y-wing/TIE Bomber)

1

1.00/1.11

1.25

25.00%

1.25/1.39

1.44

44.00%

1.44/1.60

2blue

1.5

0.83

1.83

22.00%

1.02

1.95

30.00%

1.08

1blue-black(B-wing)

1.75

1.25

2.14

22.29%

1.53

2.37

35.43%

1.69

1blue-black + Toryn

1.94

1.39

2.22

14.43%

1.59

2.41

24.23%

1.72

2black(w/o Keyan)

2

1

2.44

22.00%

1.22

2.72

36.00%

1.36

2black(Keyan)

2.5

1.25

2.84

13.60%

1.42

3.06

22.40%

1.53

The second table has efficiency calculated and sorted in descending
order. The B-wing tops the list when taken with 2BCCs and is generally more efficient in all conditions.

Efficiency

B-wing + Toryn + 2BCC

1.72

B-wing + 2BCC

1.69

TIE Bomber + 2BCC

1.6

B-wing + Toryn + BCC

1.59

B-wing + BCC

1.53

Keyan + 2BCC

1.53

Y-wing + 2BCC

1.44

Keyan + BCC

1.42

TIE Bomber + BCC

1.39

...

For
B-wings, both 1BCC and 2BCC bring enough damage to be taken into
consideration, although the first BCC brings the bigger boost in efficiency. I also considered B-wings with Toryn Farr nearby. As
expected, Toryn Farr is weaker than a Bomber Command Center for an
anti-ship of 1blue 1black. Of surprise is that the efficiency of an
X-wing with 2 Bomber Command Centers is higher than that of a Vanilla
Firespray!

To remember: Bomber Command Center transforms your mediocre bombers into decent bombers and good bombers into great bombers!

Cost of Flotillas

But let's not get ahead of ourselves! Flotillas cost too, right? So you could argue that efficiency of squadrons has to take into account the cost of those flotillas with Bomber Command Center, 26 pts minimum for the Rebels and 31 pts for the Empire.

In the following table I have filled 134 points with a single squadron type and calculated the damage. Unrealistic, I know, but the point I'm going to make after this remains unchanged..

Squadrons

Points

Avg

Efficiency

Fleet of 13 Y-wings

130

13

1

13 Y-wings + BCC

156

16.25

1.04

13 Y-wings + 2 BCC

182

18.72

1.03

Fleet of 9 B-wings

126

15.75

1.25

Fleet of 9 B-wings + BCC

152

19.26

1.27

Fleet of 9 B-wings + 2 BCC

178

21.33

1.2

Fleet of 10 X-wings

130

7.5

0.58

Fleet of 10 X-wings + BCC

156

10.3

0.66

Fleet of 10 X-wings + 2 BCC

182

11.5

0.63

Fleet of 14 TIE Bombers

126

14

1.11

Fleet of 14 TIE Bombers + BCC

157

17.5

1.11

Fleet of 14 TIE Bombers + 2 BCC

188

20.16

1.07

Fleet of 7 Firesprays

126

10.5

0.83

Fleet of 7 Firesprays + BCC

157

12.81

0.82

Fleet of 7 Firesprays + 2 BCC

188

13.65

0.73

It seems that the efficiency is unchanged when taking this into account! So we end up paying the same per point of average damage as before! So what have we gained?

Activations, a flotilla is an extra activation on the battlefield

Points for squadrons beyond the 134 point mark, because flottillas can "carry their weight" by directly enhancing squadron damage

Decreasing variance of squadron rolls considerably: Even if the B-wings + flotillas generate the same average damage, the risk of blanks is removed

Extra anti-squadron fire

By having more damage per squadron, we concentrate firepower.

There's certainly things to lose:

Flotillas might be a liability since only one accuracy can ruin their day

More damage per squadron also means that you lose a lot of firepower for the same amount of HP lost. Individual squadrons are more important, because if you've only flotillas left, you can't do any damage with them.

Conclusions

This went a bit beyond a simple math article, since there are some lessons to be learned from this. Namely, thattaking flotillas with BCC further increases your investment in bomber squadrons without increasing their efficiency, but eliminating variance. I admit I thought of flotillas with BCC as a damage multiplier, but it's more akin to a damage focusing element. You get more damage in per squadron activation and with less variation, this is incredibly valuable.

Correction: The second paragraph was a mess and I put 8 points for all my TIE Bomber calculations. Shows how much I play Empire, right?